The common invariant subspace problem: an approach via Gr�bner bases
نویسندگان
چکیده
منابع مشابه
The Invariant Subspace Problem
Notes for my lectures in the PSU Analysis Seminar during the winter and spring terms 2013-14, with special emphasis on the 1972 results of Victor Lomonosov.
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The notion of an invariant subspace is fundamental to the subject of operator theory. Given a linear operator T on a Banach space X, a closed subspace M of X is said to be a non-trivial invariant subspace for T if T (M) ⊆M and M 6= {0}, X. This generalizes the idea of eigenspaces of n×n matrices. A famous unsolved problem, called the “invariant subspace problem,” asks whether every bounded line...
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Heeft elke begrensde lineaire operator, werkend op een Hilbert ruimte, een niet-triviale invariante deelruimte? Het antwoord is positief voor zowel eindig-dimensionale ruimtes als voor niet-separabele ruimtes. Het onopgeloste probleem voor het geval daar tussenin, dus voor separabele Hilbert ruimtes staat bekend als het invariante deelruimte probleem. Professor B.S. Yadav van de Indian Society ...
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This article presents a computable criterion for the existence of a common invariant subspace of n×n complex matrices A1, . . . , As of a fixed dimension 1 ≤ d ≤ n. The approach taken in the paper is model-theoretic. Namely, the criterion is based on a constructive proof of the renowned Tarski’s theorem on quantifier elimination in the theory ACF of algebraically closed fields. This means that ...
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In [1], J. Dyer, A. Pedersen and P. Porcelli announced that an affirmative answer to the invariant subspace problem would imply that every reductive operator is normal. Their argument, outlined in [1], provides a striking application of direct integral theory. Moreover, this method leads to a general decomposition theory for reductive algebras which in turn illuminates the close relationship be...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00858-9